In the RPS formalism, the variables pressure \(p\)  and volume \(v\)  are not used because of changing their meanings in the holographic viewpoint. On the other hand, two quantities \(C\)  and \(\mu \)  play a an important role in the context of conformal field theory (CFT). Since the central charge \(C\)  determines the number of degrees of microscopic freedom in CFT, its conjugate \(\mu \)  is considered as a chemical potential [1]}. The first law of thermodynamics for a Taub-NUT-AdS black hole in RPS formalism is written as
\(dM=T dS+\tilde{\phi }_e d\tilde{Q}_e+\tilde{\phi }_m d\tilde{Q}_m+\mu dC.\) 
